A circuit with an ideal OPAMP is shown in the figure. A plus $V_{\text {IN }}$ of 20 ms duration is applied to the input. The capacitors are initially uncharged.

For an $n$-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity ( $\partial V_T / \partial\left|V_{B S}\right|$ ) is found to be $50 \mathrm{mV} / \mathrm{V}$ at a substrate voltage $\left|V_{B S}\right|=2 \mathrm{~V}$, where $V_T$ is the threshold voltage of the MOSFET. Assume that, $\left|V_{B S}\right| \gg 2 \phi_B$, where $q \phi_B$ is the separation between the Femi energy level $E_F$ and the intrinsic level $E_i$ in the bulk. Parameters given are

Electron charge $(q)=1.6 \times 10^{-9} \mathrm{C}$

Vacuum permittivity $\left(\varepsilon_o\right)=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}$

Relative permittivity of silicon $\left(\varepsilon_{S i}\right)=12$

Relative permittivity of oxide $\left(\varepsilon_{o x}\right)=4$

The doping concentration of the substrate is

The autocorrelation function $R_X(\tau)$ of a wide-sense stationary random process $X(t)$ is shown in the figure.

$$ \text { The average power of } X(t) \text { is ___________} $$

Consider a super heterodyne receiver tuned to 600 kHz . If the local oscillator feeds a 1000 kHz signal to the mixer. The image frequency (in integer) is $\_\_\_\_$ kHz .